It's a truism that having a baby changes everything. But that "everything" isn't generally thought to include your leadership priorities or the way people in your company are paid. Yet new research shows these kinds of shifts may be part and parcel of becoming a dad--especially if your child is a girl.

The most recent evidence comes from a study of the Supreme Court. Maya Sen and Adam Glynn, professors at the University of Rochester and Harvard University, respectively, studied 990 Supreme Court cases that involved gender issues. The researchers found that among judges who had one child, those with a daughter were 16 percent more likely to decide cases in favor of women’s rights. The effect was stronger on judges appointed by Republican Presidents (and therefore thought to be more conservative) than it was on judges appointed by Democratic Presidents.

The researchers also looked at about 3,000 appellate cases that did not appear to involve gender. In those cases, having a daughter (as compared to a son) didn't seem to make a difference in a judge's rulings. "By having at least one daughter, judges learn about what it's like to be a woman, perhaps a young woman, who might have to deal with issues like equity in terms of pay, university admissions or taking care of children," Sen told the New York Times.

Better Pay for Women

The Supreme Court study is just the latest to show that having a daughter affects dads in ways they may not anticipate. The Washington Post, in writing about Sen and Glynn's research, notes that previous studies "found a link between having daughters and holding more liberal views in the general population." Research from Yale has shown that U.S. legislators are more likely to vote in favor of reproductive rights if they have daughters.

As for founders and CEOs, a study of Danish companies showed that male CEOs actually started to pay their female employees more after they became dads to daughters. Firstborn daughters had the most influence--at their dad's companies, the wage gap (the amount similarly qualified women and men are paid for similar work) closed by three percent after they were born.

In this case, it's interesting to note that the women who benefitted the most were highly-educated. Perhaps that’s because these ambitious and affluent men found it easier to envision their own daughters someday walking in those women's shoes.

And it was the CEOs of companies with between 10 and 50 employees who were most likely to start making changes (those with fewer than 10 employees were not included in the study). The researchers believe this is because at smaller companies, leaders have more direct influence over how much their employees are paid.

So, how, as a leader, can you approach fairness for everyone? After all, not everyone will have a girl--and we don’t know much at all about how women leaders change after becoming moms to boys.